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Resource-Bounded Strong Dimension versus Resource-Bounded Category
 

Summary: Resource-Bounded Strong Dimension versus
Resource-Bounded Category
John M. Hitchcock a
and A. Pavan b,1
aDepartment of Computer Science, University of Wyoming,
jhitchco@cs.uwyo.edu
bDepartment of Computer Science, Iowa State University,
pavan@cs.iastate.edu
Abstract
Classically it is known that any set with packing dimension less than 1 is meager
in the sense of Baire category. We establish a resource-bounded extension: if a class
X has -strong dimension less than 1, then X is -meager. This has the applica-
tions of explaining some of Lutz's simultaneous -meager, -measure 0 results and
providing a new proof of a Gu's strong dimension result on infinitely-often classes.
Key words: computational complexity, resource-bounded category,
resource-bounded dimension, resource-bounded measure
1 Introduction
The most common mathematical notions of size and dimension now have
resource-bounded versions that are useful for complexity classes. We use to
denote a resource bound such as p (polynomial time) or pspace (polynomial

  

Source: Aduri, Pavan - Department of Computer Science, Iowa State University

 

Collections: Computer Technologies and Information Sciences